Some asteroids and comets are non-spherical. But is the nature of big things and gravity so that large things in the universe are always spherical? What is the biggest astronomical object in terms of volume out there that's not spherical?

Hint: The more an object spins, the less of a true sphere it is.
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called2voyage♦Nov 14 '13 at 20:12

Also, collisions and explosions can create some interesting shapes. I guess it depends on what you consider to be a single object. Nebulae are not spherical.
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called2voyage♦Nov 14 '13 at 20:25

Perhaps a better question is what is the largest (almost) spherical object?
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MoriartyNov 14 '13 at 22:09

You may be interested in the hydrostatic equilibrium, which is where an object over time will become spherical due to its own gravity. This equilibrium is dependent on multiple factors such as density, temperature and diameter.
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frodeborliJan 9 '14 at 22:54

8 Answers
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The largest sub-galactic astronomical object (in volume) that we know of is the Carina Nebula, which is a non-spherical diffuse nebula. The Carina Nebula has a radius of about 100 parsecs.

Image credit: ESA

If you consider astronomical objects of the galactic scale, then the galaxy IC 1101 is the largest astronomical object (in volume) that we know of. From Wikipedia:

The galaxy has a diameter of approximately 6 million light years, which makes it currently (as of 2013) the largest known galaxy in terms of breadth. It is the central galaxy of a massive cluster containing a mass (mostly dark matter) of roughly 100 trillion stars. Being more than 50 times the size of the Milky Way and 2000 times as massive

IC 1101 is on the left in the image below.

Here is an image from the Sloan Digital Sky Survey (SDSS) of IC 1101:

I'll leave it to you to decide if an elliptical galaxy counts as "spherical" or not.

If you don't count elliptical galaxies, the largest spiral galaxy is NGC 262, pictured below. It has a diameter of 1.3 million light years.

The "correct" link is to the conference proceedings on ArXiv, where the abstract tells you that for at a certain redshift range, a subset of gamma-ray bursts concentrates in the same angular position in the sky (14 bursts out of a total of 31 in that redshift range), when compared to bursts at other redshift ranges. That angular space is apparently 1/8 of the sky, so pretty big.
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EvertDec 16 '13 at 11:38

The largest non-spherical objects which are virialized (meaning essentially dynamically relaxed; not in the process of forming or collapsing) are super clusters of galaxies (here is a list of nearby super clusters). They're the most massive objects before you must begin to consider large scale structures like filaments.

These objects are largely non-spherical. Most of them happen to be tri-axial ellipsoids (either footballs, frisbees, or somewhere in between) due to the nature of large scale structure formation occurring along two axes at different times.

If you think tri-axial ellipsoids are just spheres squashed in certain ways (and that therefore clusters don't really count as "non-spherical"), then the answer would be filamentary structures (both the most massive, and the largest in scale). Here's an image from the Millennium Simulation to show what a super cluster would look like:

I think, by his mention of asteroids, that the OP means an object in the scale of asteroids or dwarf planets, that is, almost-solid objects. In this case, asteroids the size of 2 Pallas or 4 Vesta are ellipsoids, and smaller than that, we have 511 Davida which is the biggest clearly non-spherical asteroid:

Let me see, some objects are listed because of their records. First, nebulae, which are huge clouds of dust and gas. The largest in the Milky Way's neighborhood is the Tarantula Nebula (30 Doradus, NGC 2070 or Caldwell 103).:

This is the largest nebula in the Milky Way's neighborhood, at 300 light-years (almost 100 pc). But if we are in the universal record, that would be NGC 604, which is 740 light-years (240 pc) across.:

Next, galaxies, which come in different shapes. Spirals first, and what like called2voyage has said, is NGC 262. Because he can't provide a pic, I will!:

NGC 262 is a giant Seyfert spiral, and is 1.3 million light-years across, more than two times larger than the mistakenly clamed largest spiral last January 2013, NGC 6872.:

I don't know why they claimed this one as largest, at 522,000 light-years across only is less than half as that of NGC 262.

But the hands-down king of all galaxies is IC 1101, at 5.6 million light-years across, and is the record holder since 1989.:

A size comparison of this monster:

Next, structures. aneroid has the right answer. It's name is Hercules-Corona Borealis Great Wall, some 10 billion light-years across.

All these answers are, of course, correct. I only want to make a simple observation. According to the definition linked in the OP, an astronomical object is gravitationally bound. So we are looking for the largest gravitationally bound object.

If the universe were closed, it's bound and hence the largest astronomical object ;-)

However, it appears the universe is expanding forever and hence not bound. The largest bound objects are galaxy clusters and galaxy super clusters. These objects have just formed or are still forming: the dynamical (orbital) time scale at their outskirts is comparable to the age of the universe.

Thus, the largest bound objects will be larger if you wait a few giga years ...

Warning: citations above about IC 1101 being the largest known galaxy are probably wrong! Wikipedia's claimed 5 Mly size is certainly incorrect.

The visible light extent is about 360 kly (NED's summary page gives a major diameter of 1.2' and a redshift of z=0.077947, for a physical size of around 115 kpc, or 370 kly). The largest measurement one could reasonably suggest for IC 1101 (around 500 kpc, or 1.5 Mly) comes from the maximal measured extent of the diffuse light from Uson, Bough & Kuhn (1991). That's not what one usually thinks of when talking about the "size" of a galaxy. Usually we refer to the radius in which most of the visible light is enclosed, not the maximum distance we could possibly measure light that might be associated with the galaxy.

Similarly, NGC 262 is not 1.3 Mly across. It has an extended cold Hydrogen gas halo of around 600 kly (~10' HI measurement from Morris & Wannier 1979, distance ~65 Mpc), but the physical extent of its stars is around 66 kly: large for a spiral, but not huge.

To answer the question: I'd go with galaxy superclusters as being the largest currently gravitationally-bound objects in the universe.